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Block #2,280,212

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/3/2017, 4:03:41 AM Β· Difficulty 10.9563 Β· 4,552,445 confirmations

2CC
Cunningham Chain of the Second Kind

A sequence where each prime is double the previous prime minus one.

Block Header
Block Hash
52b660165cb01f6114e6e4e8fb87105fbb355af48576929259ccd4f867059aa7
View on Chainz β†—

Height

#2,280,212

Difficulty

10.956258

Transactions

1

Size

200 B

Version

2

Bits

0af4cd4e

Nonce

1,020,092,437

Timestamp

9/3/2017, 4:03:41 AM

Confirmations

4,552,445

Mined by

⛏️ P2SHAGunVUZSnHDVPMk9QT5yfxMJtZEsszpFkb

Merkle Root

b1f4173ab8007c4164fca50377d29300fa661e0cd5ccdb0ada7b2860a12b72d3
Transactions (1)
Coinbaseb1f4173ab8007c…7b2860a12b72d3
1 in β†’ 1 out8.3200 XPM110 B
AGunVUZS…EsszpFkb
Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) β€” it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

2.482 Γ— 10⁹⁴(95-digit number)
24820935772156860461…42362150177236852001
Discovered Prime Numbers
p_k = 2^k Γ— origin + 1

These are the actual prime numbers discovered by this block, computed using the verified Primecoin formula. Each number has been independently confirmed to pass the Fermat primality test. Use the FactorDB links to verify any number independently.

1
origin + 1
2.482 Γ— 10⁹⁴(95-digit number)
24820935772156860461…42362150177236852001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
4.964 Γ— 10⁹⁴(95-digit number)
49641871544313720922…84724300354473704001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
9.928 Γ— 10⁹⁴(95-digit number)
99283743088627441844…69448600708947408001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.985 Γ— 10⁹⁡(96-digit number)
19856748617725488368…38897201417894816001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.971 Γ— 10⁹⁡(96-digit number)
39713497235450976737…77794402835789632001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
7.942 Γ— 10⁹⁡(96-digit number)
79426994470901953475…55588805671579264001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.588 Γ— 10⁹⁢(97-digit number)
15885398894180390695…11177611343158528001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.177 Γ— 10⁹⁢(97-digit number)
31770797788360781390…22355222686317056001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
6.354 Γ— 10⁹⁢(97-digit number)
63541595576721562780…44710445372634112001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.270 Γ— 10⁹⁷(98-digit number)
12708319115344312556…89420890745268224001
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 10 consecutive prime numbers forming a Cunningham Chain of the Second Kind. The prime chain origin β€” the large number shown above β€” anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

β˜…β˜…β˜†β˜†β˜†
Rarity
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

How Primecoin's Proof-of-Work Constructs These Primes

Primecoin stores a value called the prime chain origin in each block. The miner found a large integer such that when divided by a primorial (the product of small primes: 2 Γ— 3 Γ— 5 Γ— 7 Γ— …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial β€” that divisibility is part of the proof.

Prime Chain Origin = First Prime Γ— Primorial (2Β·3Β·5Β·7Β·11·…)
Source: Primecoin prime.cpp β€” CheckPrimeProofOfWork()

This is why the origin has many small prime factors β€” those factors are the primorial divisor. The chain then extends from the first prime using the 2CC formula:

2CC: p₁ (first prime), pβ‚‚ = 2p₁ βˆ’ 1, p₃ = 2pβ‚‚ βˆ’ 1, …
Cross-reference on Chainz Explorer
Circulating Supply:57,905,407 XPMΒ·at block #6,832,656 Β· updates every 60s
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